For a current to flow due to the rotation, there needs to be a rotating part and a stationary part to the circuit.

When the disc is connected to a meter and the {Edit - I just read this - it's nonsense {magnet is rotated}??? durrr] disc is rotated, there is a emf induced by the disc's motion relative to the magnet.

If magnet and disc rotate, there is an EQUAL emf induced in the stationary connecting wires but none in the disc. The value of emf is the same, because of a very valid argument involving line integrals around the circuit and the interaction with the whole of the field around the magnet, This emf is in the opposite direction.

If the magnet, alone, rotates, the total emf around the circuit adds up to zero. The emfs balance out.

There is no paradox if you consider the whole circuit.